Do Canadians follow the British in saying 'I need to go to hospital', or do they say "He needs to go to the hospital'?
As the commenters have pointed out, both in hospital and in the hospital are valid in British English, depending on whether one is referring to a status or to a location or building. American English does not license in hospital the same way it does many others, like in school, in church, in jail, in rehearsal, and so on.
Canadian English does, or at least appears to in formal writing. Just doing a web search on "in hospital" for .ca domains turns up many examples from different parts of the country:
He sustained injuries that required treatment in hospital. (Ontario Human Rights Commission)
[A] maternity questionnaire was mailed to women who had been in hospital to deliver a baby. (British Columbia Ministry of Health)
While you are in hospital, specific investigative and treatment procedures may be necessary. (Health Sciences Centre Winnipeg)
Following 130 days in hospital, five-year-old Maeve Field was discharged on July 18 … The five-year-old celebrated her birthday in hospital. CBC
But in the hospital for the same sense, as in the American fashion, is not uncommon either. In fact, I came across some articles and publications that seem to mix them.
This law says that in certain cases a doctor can decide to keep you in the hospital, even if you want to leave.… If your doctor has signed a Form 1, you must stay in hospital for up to 72 hours to be assessed (checked) by a psychiatrist. (from a University Health Network brochure, Ontario)
A stay in the hospital can be difficult for a child at any age…. While they are in hospital, children may miss their friends and family. (from AboutKidsHealth.ca)
Community Legal Education Ontario (CLEO) sponsors a legal help site called StepsToJustice.ca, which has dozens of examples of each.
Web searches are not the best, especially because in hospital may appear in things like headlines, and include results for in-hospital. For a more curated set, I searched the Strathy corpus of Canadian English, covering a sampling of CanE from the 1980s to the present. It at least confirms that in hospital is not unknown in present-day Canadian fiction, journalism, and academia: being in hospital, staying in hospital, people in hospital, and so forth all have results, whereas none are found in COCA except when quoting British people. In fact, admitted to hospital, with 65 results, appears four times as often as admitted to the hospital does.
Since the posted question asks about the specific phrase "go to hospital," I ran a search of the Corpus of Canadian English (Strathy), using the link in choster's answer, for instances of the phrase "to hospital." In response, Strathy returned 427 matches, the vast majority of which involved relevant situations where a U.S. English speaker would have been more likely to say "to the hospital."
Among Strathy's matches were instances of the following expressions:
admitted to hospital
airlifted to hospital
bring the girl to hospital
called again to hospital
came to hospital
delivered us to hospital
flown to hospital
go to hospital
got him to hospital
made it to hospital
moved to hospital
presented to hospital
readmitted to hospital
returned to hospital
rushed to hospital
sent to hospital
taken [or took] to hospital
transported to hospital
transferred to hospital
went to hospital
Instances of the "go to hospital" family of variants were fairly rare—only about a dozen altogether (including instances of "went to hospital"), which is considerably fewer than were recorded for the most popular phrases: "admitted to hospital," "rushed to hospital," "sent to hospital," and "taken to hospital."
Variants on the simple "go to hospital" (which appeared only once in its simplest form in the corpus results) included the following:
would only go to hospital
had to go to hospital
needed to go to hospital
going to hospital
went to hospital
In any event, it seems clear that use of the phrasing "to hospital" in instances where U.S. English speakers would say "to the hospital" is widespread among Canadian English speakers, although they are not especially partial to "go" as the antecedent verb.